Question

The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I₀. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

(a) I₀ + ML²/2

(b) I₀ + ML²/4

(c) I₀ + 2ML²

(d) I₀ + ML²

Answer 1

Correct option (b) I₀ + ML²/4

Explanation:

 According to the theorem of parallel axes, the moment of inertia of the thin rod of mass M and length L about an axis passing through one of the ends is

I = I_CM + Md²

where I_CM is the moment of inertia of the given rod about an axis passing through its centre of mass and perpendicular to its length and d is the distance between two parallel axes.